Question: Given $ m \angle CBD = 9x + 64$, and $ m \angle ABC = 2x + 61$, find $m\angle CBD$. $B$ $A$ $D$ $C$
Explanation: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {2x + 61} + {9x + 64} = {180}$ Combine like terms: $ 11x + 125 = 180$ Subtract $125$ from both sides: $ 11x = 55$ Divide both sides by $11$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $m\angle CBD$ $ m\angle CBD = 9({5}) + 64$ Simplify: $ {m\angle CBD = 45 + 64}$ So ${m\angle CBD = 109}$.